It has been a source of enduring fascination for archaeologists and amateur Egyptologists everywhere: what exactly happened to the sarcophagus of Menkaure, one of Egypt's greatest Pharaohs? Now, more than 170 years after it was found and lost, the mystery could be solved.

Built from polished blue basalt to transport the king's earthly remains to the next world, the elaborately decorated vessel lay hidden inside the third-largest of Giza's renowned Pyramids for more than 4,000 years. In 1837 the British colonel Richard William Howard Vyse blasted his way into Menkaure's sepulchral chamber using gunpowder and discovered the stone casket.

The mummy was missing by that time — ancient Arabic graffiti indicated that the colonel was not the first to find the chamber — and he realised that his discovery could open the way for a new generation of grave robbers. “As the sarcophagus would have been destroyed had it remained in the Pyramid,” he noted in his diaries, “I resolved to send it to the British Museum.”

In a twist worthy of an Indiana Jones film, the sarcophagus was lost again the following year before it could reach British shores. The merchant ship Beatrice, which was carrying it and other antiquities found by the archaeologist, sank while sailing from Malta to Gibraltar — reportedly off the coast of Spain, near Alicante.

Now the Egyptian Government wants to recover it with the aid of underwater robots. Zahi Hawass, who heads Egypt's Supreme Council for Antiquities, told Spanish journalists that he was seeking financing from the National Geographic Society for the search.

To locate the Beatrice he has lined up the services of Robert Ballard, who found the Titanic using high-tech submersibles. The Egyptians have also privately suggested Franck Goddio, the French marine archaeologist who has discovered hundreds of artefacts from submerged parts of Alexandria.

“I will seek a formula for co-operation with the Spanish Government and we will agree to return the sarcophagus to Egypt,” Dr Hawass said. Experts say that finding the ship will not be easy. In his account of the expedition Colonel Vyse noted that the Beatrice “was supposed to have been lost off Carthagena . . . as some parts of the wreck were picked up near the former port”. Other accounts say that the crew swam safely to shore, suggesting that the Beatrice lies in shallow water. Still others merely state that it went missing somewhere between Malta and Gibraltar — an impossibly large area to search.

“It's going to be very challenging to find something of that sort,” said John Baines, Professor of Egyptology at Oxford University. “Looking for something in the open Atlantic, which is nearly what this amounts to, strikes me as being a hopeless case.”

Dr Hawass is undeterred. “We have all the information from the time the ship sank, from Spanish newspapers and other sources,” he said. The Egyptian Ambassador in Madrid met Spanish officials this month to seek their co-operation in the project.

However, Spain is locked in a legal battle over a sunken treasure worth an estimated $500million (£256million) with the company that found and recovered it, the US-based Odyssey Marine Exploration. Spain is arguing that Odyssey looted one of its naval ships, Nuestra Señora de las Mercedes, which was sunk by the British fleet off the coast of Portugal in 1804, laden with gold and silver coins.

Some believe that Menkaure's sarcophagus being on a British vessel could complicate Spain's legal argument at a crucial moment. There is also the question of who would get the spoils if they were to be raised from the deep.

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